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Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond

Ajit C. Balram, Maissam Barkeshli, and Mark S. Rudner
Phys. Rev. B 99, 241108(R) – Published 19 June 2019
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Abstract

The Read-Rezayi (RR) parafermion states form a series of exotic non-Abelian fractional quantum Hall (FQH) states at filling ν=k/(k+2). Computationally, the wave functions of these states are prohibitively expensive to generate for large systems. We introduce a series of parton states, denoted 2¯k1k+1, and show that they lie in the same universality classes as the particle-hole-conjugate RR (“anti-RR”) states. Our analytical results imply that a [U(1)k+1×U(2k)1]/[SU(k)2×U(1)1] coset conformal field theory describes the edge excitations of the 2¯k1k+1 state, suggesting nontrivial dualities with respect to previously known descriptions. The parton construction allows wave functions in anti-RR phases to be generated for hundreds of particles. We further propose the parton sequence n¯2¯214, with n=1,2,3, to describe the FQH states observed at ν=2+1/2, 2+2/5, and 2+3/8.

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  • Received 11 February 2019

DOI:https://doi.org/10.1103/PhysRevB.99.241108

©2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ajit C. Balram1, Maissam Barkeshli2, and Mark S. Rudner1

  • 1Niels Bohr International Academy and the Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
  • 2Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20472, USA

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Issue

Vol. 99, Iss. 24 — 15 June 2019

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